Solving Frouier Series Problem: Finding Partial Sums for Periodic Function

[hazim]

[SOLVED] Frouier series problem

Lately I took Frouier series...

Homework Statement

Find the Fourier series of the function below which is assumed to have the period 2 $$\pi$$, and find the first three partial sums.

http://www.imagehosting.com/out.php/i1650739_untitled.JPG

Homework Equations

The Attempt at a Solution

I used office 2007 to write my solution...and here they are hosted as a picture..
http://www.imagehosting.com/out.php/i1650792_untitled1.JPG

I see my answer not correct, I hope someone helps me..Thanks

 

[G01]

You are correct to integrate from -pi to pi in the integral, but your function is non-zero over that entire interval, so I do not know why you have the function value as 0 in $$[-\pi , -\pi/2]$$ and $$[\pi/2 , \pi]$$.

Also I believe your constant in front of your integral for a_n is incorrect. The constant in front of that integral should be:

$$\frac{2}{Period}=\frac{2}{2\pi}=\frac{1}{\pi}$$

 

[hazim]

sorry, there is a wrong in the picture of the function...the correction is
-2Pi becomes -Pi; -Pi becomes -Pi/2; Pi becomes P/2; and 2Pi becomes Pi.

so 'GO' the 0's in the integrals you specified becomes right with me..and you are correct about a_n, it should be 1/Pi and the same in the denominator of the cosine in that line..

 

[G01]

sorry, there is a wrong in the picture of the function...the correction is
-2Pi becomes -Pi; -Pi becomes -Pi/2; Pi becomes P/2; and 2Pi becomes Pi.

so 'GO' the 0's in the integrals you specified becomes right with me..and you are correct about a_n, it should be 1/Pi and the same in the denominator of the cosine in that line..

OK your integration makes sense then.

BTW. I usually imagine my PF name being pronounces "G Zero One."

So, was the constant your problem or do are you still having trouble?

 

[hazim]

yes it was the constant..it's now solved..thanks

 

[G01]

Glad to be of help.